New

Year 9

Multiples of 10 involving negative exponents

I can write any integer in a range of forms.

Download all resources

Share activities with pupils

New

Year 9

Multiples of 10 involving negative exponents

I can write any integer in a range of forms.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

View new resources

Slide deck

Download slide deck

Skip slide deck

Lesson details

Key learning points

A positive exponent tells you how many identical values must be multiplied together.
Dividing by 10^n is the same as multiplying by its reciprocal.
A negative exponent tells you how many reciprocals of the base must be multiplied together.
a^(−3) = 1/a^3

Keywords

Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

Common misconception

A negative exponent implies that the entire value is negative.

Refer back to the table showing the structure of how the negative exponents occur and highlight that none of the decimal values are negative.

To help you plan your year 9 maths lesson on: Multiples of 10 involving negative exponents, download all teaching resources for free and adapt to suit your pupils' needs...

Ensure that you have place value grids accessible with the exponents of 10 included.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

Skip lesson video

Worksheet

Download worksheet

Skip worksheet

Starter quiz

Download starter quiz

6 Questions

Q1.

A prime number is an integer greater than one with exactly factors.

Correct Answer: 2, two

Q2.

Which of the following products only use prime numbers?

Correct answer: 2 × 2 × 13

2 × 6 × 13

2 × 9 × 13

Correct answer: 2 × 3 × 5 × 17

Q3.

Write 300 as a product of its prime factors.

4 × 3 × 25

Correct answer: 2² × 3 × 5²

4 × 3 × 5²

2² × 3 × 25

2² × 3 × 5

Q4.

Use the fact that 60 = 2² × 3 × 5 to write 300 as a product of its prime factors.

2² × 3² × 5

Correct answer: 2² × 3 × 5²

2² × 3² × 5²

2 × 3 × 5²

Q5.

Use the fact that 60 = 2² × 3 × 5 to write 30 as a product of its prime factors.

2² × 3 × 5 ÷ 2

Correct answer: 2 × 3 × 5

2² × 5

2 × 3 × 5²

Q6.

If 52 = 2² × 13 and 175 = 5² × 7, which of the following is the most useful arrangement to calculate 175 × 52?

2 × 2 × 13 × 5 × 5 × 7

2 × 13 × 2 × 5 × 5 × 7

Correct answer: 2 × 5 × 2 × 5 × 13 × 7

2 × 7 × 2 × 5 × 13 × 5

Exit quiz

Download exit quiz

6 Questions

Q1.

A number written in exponential form represents a repeated ...

addition

division

Correct answer: multiplication

subtraction

Q2.

Match each fraction to its equivalent exponential form.

Correct Answer:

\frac{1}{10}

10^{- 1}

$10^{- 1}$

Correct Answer:

\frac{1}{100}

10^{- 2}

$10^{- 2}$

Correct Answer:

\frac{1}{1000}

10^{- 3}

$10^{- 3}$

Correct Answer:

\frac{1}{10000}

10^{- 4}

$10^{- 4}$

Correct Answer:

\frac{1}{100000}

10^{- 5}

$10^{- 5}$

Correct Answer:

\frac{1}{1000000}

10^{- 6}

$10^{- 6}$

Q3.

Match each decimal to its equivalent exponential form.

Correct Answer:

0.002

2 \times 10^{- 3}

$2 \times 10^{- 3}$

Correct Answer:

0.00004

4 \times 10^{- 5}

$4 \times 10^{- 5}$

Correct Answer:

0.2

2 \times 10^{- 1}

$2 \times 10^{- 1}$

Correct Answer:

0.005

5 \times 10^{- 3}

$5 \times 10^{- 3}$

Correct Answer:

0.000005

5 \times 10^{- 6}

$5 \times 10^{- 6}$

Correct Answer:

0.0004

4 \times 10^{- 4}

$4 \times 10^{- 4}$

Q4.

3 \times 10^{- 2} + 2 \times 10^{- 5} + 8 \times 10^{- 6}

represents the number

Correct Answer: 0.030028, 0.030 028

Q5.

Which of the following is not an alternative way of writing 2400?

24 \times 10^{2}

24000 \div 10

Correct answer:

240000 \div 10^{3}

2.4 \times 10^{3}

\frac{240}{10} \times 10^{2}

Q6.

Which of the following is not an alternative way of writing 12 000?

Correct answer:

1.2 \times 10^{3}

\frac{1200}{10^{2}} \times 10^{3}

120000 \times 10^{- 1}

1.2 \times 10^{4}

Correct answer:

\frac{120}{10^{3}} \times 10^{4}

Multiples of 10 involving negative exponents

Multiples of 10 involving negative exponents

These resources will be removed by end of Summer Term 2025.

Slide deck

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Starter quiz

6 Questions

Exit quiz

6 Questions